Are those who draw Prophet Mohammed(peace be upon him) hate-mongers?

They would not necessarily be hate-mongers although often they could qualify for the label. It depends on the motivation behind the act and whether it is done out of spite. If the person who draws the picture does not believe that it is evil to draw him and does not use the drawing to taunt Muslims it is difficult to consider the act as a form of hate-mongering. If the drawer is not aware of the taboo nature of such portrayals in the Muslim religion and culture he or she would not be considered as a perpetrator of such behaviour. Many acts are relative to the culture and settings under which they take place and would have to be essed in accordance with these other factors.